The Real Product: Particle in a 3-Dimensional Box Sept. 19, 2005

from Introduction to Quantum Chemistry· ·

We show that the product of one-dimensional functions is indeed a solution to the 3-dimensional problem. We find the energy and show that the energy and wavefunction now depend on 3 independent quantum numbers. When the box is symmetric, for example, a cube, some energy levels are degenerate. We noted that symmetry generally leads to degeneracy, though not all degeneracy is a result of symmetry (accidental symmetry). We extended the concept of the product wavefunction to systems of more than one particle. We drew a quick concept map of where we have been in the course so far. Mathematica notebook ...



We show that the product of one-dimensional functions is indeed a solution to the 3-dimensional problem. We find the energy and show that the energy and wavefunction now depend on 3 independent quantum numbers. When the box is symmetric, for example, a cube, some energy levels are degenerate. We noted that symmetry generally leads to degeneracy, though not all degeneracy is a result of symmetry (accidental symmetry). We extended the concept of the product wavefunction to systems of more than one particle. We drew a quick concept map of where we have been in the course so far.